4 Advanced Radar Systems
4.1 Pulse Compression
In Chapter 3 the determination of range resolution for a simple pulsed radar was shown as being dependent upon the pulse width, . In fact, the expression for minimum range resolution is given by the following:
Minimum range Rres¼c 2
where c is the speed of lightð3 108m=sÞ and is the pulse width (s).
There are practical limits as to how small the pulse width may be made. As was seen in Chapter 3, the theoretical receiver bandwidth required to pass all the components of a pulse of width is 2/ , or 1/ if a matched filter is used. Therefore, narrow pulses need a wider receiver bandwidth which leads in turn to more noise and a greater risk of interference.
However, perhaps more troublesome is the fact that, as the pulse width reduces, so peak power must increase to keep the average power constant. There are clearly definite physical limits as to how high the peak power can be. Therefore, to reduce the range resolution, a solution has to be sought that does not lie in the direction of ever-reducing pulse widths.
In fact, techniques exist that permit the range resolution to be determined to a much finer degree, although sophisticated modulation and signal processing has to be employed. The technique called pulse compression (sometimes colloquially known as ‘chirp’) is able to both improve range resolution and help in extracting target echoes from noise.
In pulse compression the RF carrier is not a fixed frequency modulated by the pulse envelope, rather the RF carrier is modulated with a particular characteristic. In the simplest form of pulse compression, the carrier is frequency modulated according to a linear law, in fact the carrier frequency increases in linear fashion for the duration of the transmitted pulse.
Military Avionics Systems Ian Moir and Allan G. Seabridge
# 2006 John Wiley & Sons, Ltd. ISBN: 0-470-01632-9
In Figure 4.1 the frequency increases from f1 at the pulse leading edge to f2 at the trailing edge. The target return contains virtually the same modulation within the target echo. In the radar receiver the signal is passed through a filter that has the property of speeding up the higher frequencies at the trailing edge of the pulse so that they catch up with the lower-frequency components at the leading edge. The overall effect is to compress the signal to a width of 1=B, where B is the bandwidth of the transmitted pulse, equal to f2 f1. This narrow, processed signal in fact has the form sin x=x and is also increased in power by a factor equivalent to the pulse compression ratio. Therefore, pulse compression, as well as greatly improving range resolution, also greatly increases the signal power and hence target detection. Pulse compression ratios for a practical radar system can easily be achieved in the region of 100–300 and therefore the advantages can be considerable.
It has been mentioned that the compressed pulse has the form sin x=x, the same format as for the radar antenna main beam and sidelobes. Therefore, pulse compression does have the disadvantage that it produces range sidelobes as well, and these may cause difficulties in some applications. A further potential problem can occur if the target echo contains a significant Doppler shift when range errors may be experienced.
The lower part of Figure 4.1 shows another advantage of pulse compression. In this example, two target returns are overlaid, and, using conventional signal processing, it would not be possible to discriminate between them. However, using pulse compression and the accompanying signal processing, both echoes are enhanced and may be separated.
Although linear FM pulse compression as described above is the most widely used, there are several other techniques that achieve a similar outcome. In recent years the viability and application of surface acoustic wave (SAW) technology has allowed the pulse compression process to be implemented in a cost-effective manner.
Pulse Width Target Return
Filter
Transmit Time
Frequency Return A
Return B
Return A + B
Filter
A B
f2 f1
Figure 4.1 Principle of pulse compression.
136 ADVANCED RADAR SYSTEMS
Pulse compression is used as part of the signal processing associated with synthetic aperture radar (SAR) and some advanced forms are used in active electronically scanned arrays (AESAs) where compression ratios up to 1000 may be attained using sophisticated signal processing methods.
4.1.1 Coherent Transmission
The description of the pulsed radar in Chapter 3 related to the transmission of non-coherent carrier waveforms. That is, the successive pulses of energy that were transmitted were unrelated in phase from one pulse to the next. Pulse Doppler techniques using coherent radar transmissions enable much more data to be extracted. Coherent transmission can be likened to a transmitter that is transmitting continuously while being switched in and out of the antenna (Figure 4.2).
In Figure 4.2, non-coherent transmission is shown at the top of the diagram. The transmitter is controlled by the modulator, and a series of pulses of the same duration but differing in phase is transmitted towards the target. The reflections from the target will likewise be unrelated in phase.
By contrast, the coherent transmission example shown in the lower part of the picture shows a stable local oscillator or ‘STALO’ being modulated to transmit the same series of pulses. The STALO runs continuously and an associated power amplifier is switched on and off to produce pulses of the appropriate pulse width and pulse repetition frequency (PRF).
Therefore, within these pulses, the carrier is in phase, almost as though sections of the carrier have been ‘cut’ from the same continuous wave. The reflected energy from the target largely preserves this phasing in the received target echo, and this property provides very useful features for the radar designer.
The properties and composition of a non-coherent and coherent pulse train for a carrier of frequency f0are quite different, as shown on Figure 4.3. Each pulse train comprises a series of pulses with pulse width and a pulse period of 1=fr, equivalent to a PRF of fr.
Transmitter
Transmitter Stable
Oscillator
Modulation
Modulation Non-Coherent
Transmission
Coherent Transmission
Pulses are of same duration and frequency but different in phase
Pulses are of same duration and frequency and are in phase as if having
been ‘cut’ from the same continuous wave
Figure 4.2 Comparison of non-coherent and coherent transmission.
The non-coherent pulse train transforms into a continuous sin x=x spectral waveform with bandwidth 2= , represented as a width1= centred on the carrier frequency f0.
The coherent pulse train spectral response is bounded by the same sin x=x envelope of width1= centred on the carrier frequency. However, in this case the energy is reflected by spectral lines each separated by fr, the pulse repetition frequency. In fact these spectral lines are minispectra rather than spectral lines since the length of the pulse has an important effect, as will be seen.
Figure 4.4 illustrates the effect of varying the length of a series of coherent pulses. The longer the pulse train, the narrower are the resulting frequency spectra. In each case the frequency spectrum is represented by the sin x=x profile, but, as the length of the pulse train increases, this merges to form an apparent single spectral line. In the figure above, an infinitely long coherent pulse transforms into a single spectral line. Clearly, this is not practical in reality. A long coherent pulse train transforms into a narrow sin x=x response and the short coherent pulse train into a broader response. There is obviously a trade-off needed in the design to enable the most desirable performance to be achieved, bearing in mind practical constraints that apply. In a radar system where a target echo needs to be detected, the pulse train has to be of a sensible length. On the other hand, the longer the pulse train can be made within reason, then the narrower the frequency spectrum and therefore the greater the ability to reject unwanted signals.
Figure 4.5 depicts the difference between a single pulse and a pulse train comprising eight pulses. The single pulse of length transforms into a single sin x=x spectrum of width 2=
(ignoring sidelobes). The short pulse train transforms into a series of sin x=x spectra whose width is determined by the pulse width of the pulses spaced at intervals equal to the PRF, fr. The individual spectra are bounded by a sin x=x envelope, this envelope being of width 2= , where is the length of the transmitted pulse train.
It may be seen that PRF is an important parameter in the pulse train spectrum. The lower the PRF, fr, the closer together each of the spectra will be and after a certain point the sidelobes will begin to interfere with the adjacent spectra, distorting the signal content.
Figure 4.3 Characteristics of non-coherent and coherent pulse trains.
138 ADVANCED RADAR SYSTEMS
Infinite Pulse Train
Long Pulse
Short Pulse Time
Frequency
+∝ -
∝
Figure 4.4 Effect of pulse train length.
Single Pulse
Pulse Train
t
t
fr
-fr fr
2/t
2/t
Envelope
Figure 4.5 Comparison of a single pulse and a pulse train.
The use of pulsed transmissions in this manner can therefore be used in airborne radars provided a number of criteria are satisfied. These are as follows:
1. The radar is coherent.
2. The PRF is high enough to spread the spectral lines sufficiently far apart.
3. The duration of the pulse train is sufficiently short to make the spectral lines reasonably narrow.
4. Doppler filters are devised to filter out the spectral sidelobes.
4.1.2 Fourier Transform
The Fourier series, or Fourier transform as it is often called, is a mathematical relationship that identifies all those frequency components necessary to synthesise a particular waveform.
The use of frequency-related analytical techniques is of immense importance in manipulat-ing the signals that are frequency dependent, or that comprise important target-related frequency components. The mathematical theory is described in virtually every pure mathematics textbook, or for that matter most radar textbooks, and therefore will not be expounded in this publication. Rather, the subject will be addressed in sufficient detail such that readers can comprehend the importance of Fourier techniques as they apply to radar signal processing, particularly in Doppler radar and the associated applications.
The technique called the fast Fourier transform (FFT) is a useful method for creating a series of Doppler filters to discriminate a velocity return from ground clutter. The FFT process lends itself readily to implementation using digital computing techniques and therefore is commonly used in modern digital radars for Doppler filtering, Doppler beam sharpening (DBS) and synthetic aperture radar (SAR) modes. The FFT technique is also used in electronic warfare (EW) to analyse the characteristics of the opponent’s radar systems in real time.